This is usually done after the lysis of the cells to get at the DNA - make your lysate, salt out most of the proteins, add RNase, incubate 30 min at 37 C. Then do a phenol-chloroform extraction or two, and proceed from there,

Neither of those methods will tell you if it is RNA definitively. RNA and DNA differ only in the absence of oxygen groups in the DNA that are present in RNA so they look more or less identical to a spectrophotometer. On gel electrophoresis, degraded DNA looks just like RNA - the EtBr intercalates in the same manner to both - can you post a gel picture so we can see what is going on?

It may be that you have so much RNA present that you can't get rid of it all, you could try adding more RNase and re-extracting.

RNA is essentially ignored in genomic DNA sequencing preparation protocols. Its major effect will be in misleading quantification if you are using spectrometer readings. Did your sequencing center complain about this sample?